The government is coming under pressure to reveal the full extent of its co-operation with the CIA's secret prison network and what it knew about the torture of prisoners at Guantánamo Bay, including a British resident.

MPs and the courts are seeking disclosure of documents that would shed light on how ministers and officials - including the security and intelligence agencies - responded behind the scenes to US practices they publicly abhorred.

Calls are also being made for the government to accept some Guantánamo detainees, an issue that will be on the agenda of a meeting of divided EU foreign ministers in Brussels.

Portugal and Spain have offered to take in detainees. Though other countries are reluctant to do so there is a growing view across Europe that accepting the 60 or so prisoners out of the 245 the US has agreed can be released would be one way of showing appreciation to Barack Obama for deciding to close the camp on the US base in Cuba and respect the Geneva conventions - something the Europeans have long urged Washington to do.

Obama's moves were described by the Foreign Office yesterday as "very welcome". David Miliband, the foreign secretary, has said one man that Britain would accept is Binyam Mohamed, an Ethiopian-born UK-resident incarcerated in Guantánamo.

British officials said they were engaged in urgent discussions with the US about the future of Mohamed, who has been at the centre of a long-running case in the high court. It ruled last year that an MI5 officer participated in the unlawful interrogation of Mohamed in Pakistan in 2002. In a series of judgments, Lord Justice Thomas and Mr Justice Lloyd Jones condemned as "deeply disturbing" a refusal by the US to disclose evidence about Mohamed's treatment and secret rendition to Morocco, Afghanistan, and Guantánamo Bay. They also said claims by Mohamed's lawyers that the US was refusing to release the papers because "torturers do not readily hand over evidence of their conduct" required an answer.

Miliband conceded there was an "arguable case" that Mohamed had been subjected to torture and inhuman treatment, yet he has refused to disclose information about CIA practices.

The high court judges have taken the extraordinary step of inviting the Guardian with other media groups to challenge earlier decisions to hold much of the court hearings on the case in camera.

The high court heard that the cross-party parliamentary intelligence and security committee was not given the full picture when it first questioned security and intelligence officials. It is expected to criticise the government over its approach towards the Bush administration's rendition and interrogation policies in its latest annual report, which is now being vetted by Downing Street prior to publication.

Whitehall official suggested yesterday that they had now learned the lessons. However, Andrew Tyrie, Conservative MP and chairman of the all-party group on extraordinary rendition, said: "We need to establish the truth on the US programme and UK involvement in it."

Clive Stafford Smith, director of Reprieve, the law charity which represents numerous Guantánamo prisoners, said: "The first thing to do is focus on how we can repair the damage of the past seven years. Britain should accept some of the stateless people in Guantánamo".

He referred to Ayman al-Shurafa, a Palestinian who the US says poses no threat but whom the Israelis have refused to allow back home, and Ahmed bel Bacha, an Algerian who lived in Britain. He has been threatened by Islamists in Algeria if he returns home.

"Britain could be of great assistance to Obama and at the same time show the Muslim world we have no truck with the nightmare [of Guantánamo, inhuman treatment, and secret rendition]", Stafford Smith said. "It is the moral thing to do and would actually make Britain safer".

Shaker Aamer, a Saudi national, is the other British resident in Guantánamo.